358 ON THE CHANGE OP RKFRANUIBIUTY OK LIGHT.
intensity may be represented by fid/*, p being the* refractive index in some standard substance. In passing across the stratum whose thickness is dt, suppose the fraction qdt of the light, to be absorbed, and the fraction rdt to be refiected and scattered in all directions, then
dl = -(</ + r) hit.
Integrating this equation, and supposing /„ to be the initial value of /, when t = 0, we have
I^IjrW* ........ . .................. (a).
For the sake of simplicity, suppose the body viewed in a direction nearly perpendicular to the general stirfa.ee; and of the light reflected and scattered in passing across the stratum whose thickness is dt, suppose that the fraction n would cuter the eye if none were lost by absorption, &c. Then tin* intensity of the light coming from that stratum would In; nrldt. But in getting back across the stratum whose thickness is /, the intensity is diminished in the ratio of J0 to /. Hence if 1' be the intensity of the light actually entering the eye,
dlf = nrl,rll*dt = nrl^'i^'tlt.
If we suppose the thickness of the body snttieient to develope all the colour which the body is capable of giving, the superior limit of t will be co , and we shall have
177. The colour which accompanies ordinary ivtlexion being usually but slight, I shall neglect the chromatic variations of r. It is q which is subject to extensive and apparently capricious variations, depending upon the. refrangibility of the light. Imagine two curves drawn whose abscissa1 are proportional to /i, and ordinates proportional to the ratio of / to /„ for the firsthand the ratio of /' to 70 for the second. These curves will serve to represent to the mind the composition of the light transmitted through a stratum of the body having a thickness t, and of that reflected from the body when seen in mass. It is plain that the maximum and minimum ordinates in the two curves will correspond to the same abscissa; but unless t be very small, so small as to be insufficient to bring out the colour of the medium seen by trans-